Using public key cryptography, $X$ adds a digital signature $\sigma$ to message $M$, encrypts $\langle M, \sigma \rangle$, and sends it to $Y$, where it is decrypted. Which one of the following sequences of keys is used for the operations?

To securely sign and transmit a confidential message from $X$ to $Y$:

1. Signing (Sender $X$):

   • $X$ creates the digital signature $\sigma$ using $X$'s private key so that anyone can verify it was signed by $X$, ensuring authenticity and non-repudiation.

2. Encryption for Confidentiality (Sender $X$):

   • To ensure only $Y$ can read the message and signature $\langle M, \sigma \rangle$, $X$ encrypts the pair with $Y$'s public key.

3. Decryption (Receiver $Y$):

   • $Y$ decrypts the received ciphertext using $Y$'s private key to recover the pair $\langle M, \sigma \rangle$.

4. Signature Verification (Receiver $Y$):

   • $Y$ verifies the signature $\sigma$ using $X$'s public key.

Thus, the operation sequences are:

• Encryption / Signing: $X$'s private key followed by $Y$'s public key.

• Decryption / Verification: $Y$'s private key followed by $X$'s public key.

This matches option (D).